J. A. González, L. I. Reyes, J. J. Suárez, L. E. Guerrero, and G. Gutiérrez, *Physica A* __316__, 259 (2002)

**Chaos-induced true randomness**

We investigate functions of type X_{n} = P( qz^{n}),
where P(t) is a periodic function, q and z are real parameters.
We show that these functions produce truly random sequences. We prove
that a class of autonomous dynamical systems, containing nonlinear terms
described by periodic functions of the variables, can generate random
dynamics. We generalize these results to dynamical systems with
nonlinearities in the form of noninvertible functions. Several examples
are studied in detail. We discuss how the complexity of the dynamics
depends on the kind of nonlinearity. We present real physical systems
that can produce random time-series. We report the results of real
experiments using nonlinear circuits with noninvertible I-V
characteristics. In particular, we show that a Josephson junction
coupled to a chaotic circuit can generate unpredictable dynamics.